Graph Transformations
Changes inside the parentheses move the graph sideways, outside move it up or down.
The rules
- y = f(x − h) shifts right by h. y = f(x + h) shifts left.
- y = f(x) + k shifts up by k.
- y = −f(x) reflects across the x-axis. y = f(−x) reflects across the y-axis.
- y = a·f(x) stretches vertically by a.
Watch out: Moving the wrong way for horizontal shifts.
Worked example
How does the graph of y = (x − 3)² + 2 differ from y = x²?
- x − 3 shifts right 3.
- +2 shifts up 2.
Answer: Shifted right 3 and up 2
Try it yourself
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